Inside Heath Ledger's Sleepless Nights

New York's Washington Square Park is sometimes a haven for the stray homeless to get some shut-eye, curled up on a bench somewhere. For Heath Ledger, it was a place to roam while sleep evaded him.

"He would walk early in the morning – around 6:30 a.m. or 7," says retired city-worker Tony Rivera, 52, who walks his dog in the park each day at that time, "because, he said, he always had trouble sleeping. That's why he'd come out so early in the morning."

Heath Ledger

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Once in a while, Ledger, 28, would watch the early-morning chess players in action – sometimes even joining them. He often talked about his daughter, says Rivera, who struck up a chat with the actor during one of his sleepless strolls. "He said it was a great thing, being a dad."

Ledger, the type of actor who immersed himself in his film roles, spoke in a recent interview about how work-related stress gave him insomnia. During the shooting of his last completed film, The Dark Knight, Ledger told The New York Times in November that he often took the prescribed sleeping aid, Ambien, in an attempt to coax himself into a slumber.

"Last week I probably slept an average of two hours a night," he told The Times. "I couldn't stop thinking. My body was exhausted and my mind was still going." Ledger continued to say that taking one pill had no effect on him. He'd have to take second to fall asleep, only to awake an hour later with his "mind still racing."

Partying Until Sunrise

Ledger's reported hard-partying drinking at all hours of the night may have been another way for him to try and self-medicate himself to sleep. "He partied a lot," one friend of Ledger's told PEOPLE. "He didn't really stop partying. At nights when I was going home, he was just starting. He was part of the New York scene." Another club regular recalls that Ledger would arrive at Manhattan lounge, The Beatrice Inn, at 3:30 a.m., "and he never left until sunrise."

But not home to sleep, it seems. Instead, Ledger would be out for a walk in the park and perhaps he'd play a groggy game of chess with strangers. "He didn't seem to be such a good chess player," recalls Rivera, "but I'm not sure ..."

Ledger, perhaps, wasn't interested in winning or losing. He was just trying to calm his "racing" mind so he could once and for all get some sleep as the rest of the city woke up.